In this problem, the problem of impulsive oblique stagnation-point flow on a vertical cylinder along with mixed convection heat transfer due to buoyancy forces have been solved for the first time. The fluid at rest with uniform temperature T∞ around the cylinder starts flowing toward it at strength rate of and the cylinder temperature rises to Tw at t=0, simultaneously. The governing equations induced by the impinging flow on the constant-temperature vertical cylinder at any obliqueness angle α, have been reduced to ODEs by using similarity transformations and solved numerically. Considering a sample case of incompressible flow with Re=1, =0.7, the results of Nusselt number and similarity functions of velocity and temperature distributions have been obtained for different values of time and the angle α. At the initial instants, the Nusselt number, regardless of α's magnitude, has large values, for example Nu=5.1 at τ = 0.01. As time passes, the value of the Nusselt number reduces intensely within a short period of time (until τ ≈ 0.4) and then it changes with a moderate reduction rate, so that in the steady- state situation its value reaches to the values of 0.67, 0.61 and 0.51 for obliqueness angles α=10°, 30°, 60°.